3. Calculate the expected utility of a person who has wealth W = $10000, faces a potential loss of C = $5000 with probability and has a utility index u(x) over money:

(i) = 0.01 and u(x) = x2;

(ii) = 0.01 and u(x) = x;

(iii) = 0.1 and u(x) = 2x/10000;

(iv) = 0.1 and u(x) = ln(x) with the natural base

(v) = 0.1 and u(x) = log10(x) with the base 10

Which of the above utility indexes exhibit risk aversion? Find the certainty equivalents and risk premia of the gambles in each of the above cases. Explain the similarity between cases (iv) and (v).

4. Suppose that Alice prefers $700 for sure rather than a lottery. Suppose also that she complies with Independence. ($1000 w.p. 80%; $0 w.p. 20%)

(i) Does she necessarily prefer $600 for sure rather than a lottery ($1000 w.p. 70%; $0 w.p. 30%)

(ii) Does she necessarily prefer a lottery( $700 w.p. 50%; $0 w.p. 50%) to ($1000 w.p. 40%; $0 w.p. 60%)

(iii) Does she necessarily prefer a lottery ($800 w.p. 10%; $0 w.p. 90%) to ($1000 w.p. 8%; $0 w.p. 92%)

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Lets start with question 3 i For ux x2 Expected Utility 09910000 50002 00110000 50002 09950002 00150002 09925000000 00125000000 24750000 ii For ux x E... View the full answer